Add a Touch of Original Game Theory to Spice Up Your RPG!

Note: Often the term “Game Theory” is used by gamers to refer to the GNS (Gamism, Narrativism, and Simulationism) Theory or the RPG Theory of The Forge web site. This article deals with the science of Game Theory developed in the 1940s. For more information on GNS Theory please check out The Forge.

You are planning your next gaming session and need something that will evoke role playing from your players and suspense from the scene. You do not want to railroad your players into a contrived situation, but you do want the party to face a good solid challenge with risks and potential rewards. So you decide that in the next session you are going to have the party cut a cake, help settle two traveler’s lost luggage concerns, and then go hunting for a stag unless someone would prefer to eat rabbit.

Believe it or not, all of these situations are covered in detail by Game Theory to help explain complex situations like how the United States decided upon individual state boundaries or what the global economy is going to do. The cake cutting exercise is used to study perceived fair value and is often referenced to help predict how resources will be divided amongst different groups with different values. The traveler’s dilemma is used to understand how people may or may not cooperate as well as how they will stray from rational choices in order to profit more from a situation. And the stag hunt is used to demonstrate how sometimes your decision is not right or wrong until it has been validated or dismissed by someone else’ decision.

I will not go heavily into the math behind these games. I am far from being an expert on the matter, but the more that I read about Game Theory and the games that others have designed in studying it the more I find myself putting these games into my own adventures and scenarios.

For example, with the cake cutting game the secret is to have many resources in the same area that are valued in different ways by different groups. In a fantasy setting this could be a wooded valley with a large stream and some natural caves. Elves might want to claim the valley as part of their homeland because the woods are ancient and some of the trees might be suitable habitats for their families, a human kingdom might claim the valley because it wants the stream to help irrigate farmer’s crops with, and a clan of dwarves claims the valley because they suspect that the caves may have rich iron ore veins within them.

Now how hard is it to have these three groups on the brink of war because they all are unwilling to negotiate with each other for fear of losing that which they value the most? What if the adventure is that the PCs must somehow “cut the cake” in a way that keeps all three groups happy? What if a fourth party that wants a war to erupt causes problems for the PCs? You need only to set the pieces in place upon the board and the let players’ decisions do the rest.

And that is the beauty of Game Theory games – they are all about decisions. You can create wonderful moments for role playing and strategy around them. All it takes is a little imagination and tweaking of these games to fit most settings and systems.

So check out Game Theory and some of the games designed using it. You might find that putting the theory into practice takes your own game to a whole new level.

That is my opinion on the matter. What is yours? Do you have an idea as to how a Game Theory game can be converted into an RPG adventure scenario? Be sure to share your own tips and tricks with the Gnome Stew community by leaving a comment below. Remember that the GM is a player too, so always make sure that you get your share of the fun at the table!

I just happen to have read an article on the Travelers Dilemma last week, and have been searching Amazon.com for some Intro to Game Theory books. There is also a free MIT online course on Game Theory, but I figured I would start with a book first.

I think that Game Theory would a valuable tool to a GM, as most of RPG’s have a lot to do with resource management and group cooperation. I have been hoping to explore this further and to see how I could carry some of the lessons to my RPG material.

@DNAphil – Please post a link to that free online course if you can. I’d like to check it out. The books available are still primarily text books, so they are expensive, but MIT Press often has great stuff. I like Game Theory by Drew Fudenberg and Jean Tirole.

Sarlax on February 17, 2009 at 12:23 pm

Chicken is a good game to adapt to RPGs. The quick rules are thus: two players race towards each other. The first one to swerve is the chicken, which is shameful, but if neither swerves, they collide, and collision is worse than shame. The problem is that if both players know the rules, and they each know that the other knows the rules, each has a strategy of waiting for the other player to swerve.

In an RPG, you might have two nations arming up for a war that neither can afford to fight. The king of each country has a war-mongering noble court to deal with; if a king seeks peace, he’s called a coward by everyone in the country. If they actually fight the war, both countries will be destroyed.

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Another game would be two groups who have agreed to share some resource that matures over time. If collected at the determined time, they split the product evenly. If they collect beforehand, the good is less valuable.

An example might be a harvest of magical fruit in a shared valley. It was discovered by two villages (whose mundane crops are dying) at the same time when it was just beginning to grow. Each village’s shaman figured out that the fruit reaches its full potential in three months; if harvested even one day early, it’s only 3 quarters as valuable, and its value decreases further the earlier you harvest it, so it’s best to wait.

The dilemma is that if each group waits exactly 3 months and splits it, each ends up with half the bounty, but if they steal it early, they might end up with as much as 3/4 of the bounty. Of course, you want to try to steal it before the other village does, but the earlier you steal it, the less you get.

The PCs stumble into either village and hear the people talking about the need to go steal the crop now before the other guys do. What do the PCs do? They realize that if the crop yield is reduce by theft, one or both villages may starve.

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For a quick game, try Dollar Auction. Here’s the RPG version:

An old adventurer is selling off his gear, and the prize item is Ring of Invisibility, valued at 20,000 GP. He decides to auction it to either the PCs or the NPCs, but the rules are that the highest-bidder gets the Ring, but the second-highest bidder still pays their bid. The PCs start at 100. The NPCs go to 200, then PCs to 300, etc.

The problem is obvious. When the bid is at 19,999 GP, what should you do? Well, you haven’t exceeded the value of the Ring, so that’s a good price. However, because the loser still has to pay his bid, it’s better to escalate beyond the 20,000 GP, because it’s better to pay 20,001 GP and have a ring than to pay 19,999 and not have the ring. It’s also better to pay 20,002 and get it than to pay 20,000 and not have it, etc. Both groups will end up escalating bids well beyond the ring’s value.

Once the PCs have gotten themselves into this auction, how do they get out of it?

When creating a situation for an rpg, it is important that either there is no dominating strategy or that if there is one, the outcome is undesirable. All 2-player games of perfect information have optimal mixed strategies, but in a scenario only played once having a mixed strategy is not of much benefit and most people have no idea what they are anyway or even if they had, would find them unintuitive. My gut assumption is that this applies to n-player games, but it may very well be wrong.

In normal language: When creating a campaign, have a starting situation so that it does not have an obvious solution. Make it so that simply fighting the enemy is too costly and that there is too much at stake for diplomacy to take of it. Players will have to make tough decisions, which drives good gameplay and roleplay. (Not applicable to all playing styles.)

If there is a tactical or strategic situation, make it so that there are several options and that every option costs different resources so that players have to decide what resources they hold more valuable than others, in addition to seeing which options maximise or minimise a given resource.

In short: Know game theory so as to design situations where knowing game theory is not sufficient.

If you’re looking for a book that distills all that erudite science into an easy-to-understand discourse on the subject in an entertaining and yet pretty thorough manner, this is a great start. It’s a good enough book to keep me up at night wanting to learn more and because I enjoy the author’s voice, rather than putting me to sleep with too much math and dry exposition as some science books do, if that’s any indication.

The Stray7 on February 17, 2009 at 8:05 pm

Would you be willing to illustrate the other two concepts you mentioned? I looked at the Wiki articles but they made my head swim. How would I apply the Traveler’s Dilemma or The Stag Hunt to a typical game scenario?

GeoffA on February 17, 2009 at 8:34 pm

Here’s a couple of other good game theory ideas.

1. Prisoner’s Dilemma. Classically two spies are captured by the police who don’t have enough evidence to convict them. Each spy is questioned independently and given the opportunity to give evidence against his buddy. If one gives up evidence and the other stays silent, the cooperative one is released immediately and the stubborn one is killed. If both cooperate they get lighter punishment. If both stay quiet the police will keep the spies locked up as long as they can and make life miserable until they are forced to release both spies for lack of evidence. It wouldn’t be hard to work this into a role-playing setting if several PCs get captured on some mission of sneakery.

2. Convoy vs. U-Boats. The convoy wants to get as many ships as possible from point A to point B. The u-boats want to prevent this. You can either sail straight across the ocean or take a longer route to the north. If you take the northern route, you’ll lose some ships to ice bergs and storms so you’d rather go direct. Except the u-boats know you want to go direct so they’re more likely to be waiting there. Should the u-boats split their forces and have a weak ambush along both routes or try to guess and have a killer ambush in one place. Again, this could easily be adapted to a game setting.

I happen to be a math teacher when I’m not gaming so I have a handful of books on this topic. I’ll poke around my office tomorrow and post some titles if people are interested though they may be textbooky and not very exciting reads.

There’s a complete course of 24 video lectures on game theory, by Yale Economics Professor Benjamin Polak, here. (There’s also apparently a course on Starcraft strategy as well, if anyone’s interested.)

With Patrick’s permission, I am turning off comments on this two-year-old article because for unknown reasons it attracts a lot of spam (which we then have to manage).

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